Question
Download Solution PDFIf a > 0 and b > 0 and a + b = 1, then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Let x1, x2, ..., xn ∈ R then,
- The arithmetic mean of x1, x2, ..., xn is defined by
- The geometric mean of x1, x2, ..., xn is defined by
- The harmonic mean of x1, x2, ..., xn is defined by
- Arithmetic-Geometric mean inequality:
≤
Calculations:
Given, a > 0 and b > 0 and a + b = 1,
⇒
⇒
⇒
Now, a2 + b2 = (a + b)2 - 2ab
⇒
Now consider,
∴
Hence, the correct answer is option 3)
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